As described in Japanese Published Unexamined Patent Application Hei 6-231400, for example, this type of apparatus finds a suitable vehicle separation at the present time based on the speed of a preceding vehicle, the deceleration of the preceding vehicle, the speed of a driven vehicle (vehicle being controlled), the maximum deceleration of the driven vehicle, and the like (in the prior art, the suitable vehicle separation corresponds to the vehicle separation at the present time, but the suitable vehicle separation in the present invention described below corresponds to a vehicle separation predicted for the future and is different from in the prior art), and it generates a warning when the actual vehicle separation is smaller than the suitable vehicle separation. In addition, this apparatus sets the suitable vehicle separation as “a separation such that there is not a collision in the case when the driven vehicle decelerates at a prescribed deceleration after a time lag τ after the start of deceleration of the preceding vehicle at a prescribed deceleration”. Namely, on the assumption that the driven vehicle decelerates after the start of deceleration of the preceding vehicle, an alarm is generated when it is predicted that the vehicle separation when the two vehicles are closest is zero or becomes a certain margin (margin distance).
However, in the above-described conventional apparatus, since an alarm is generated when it is predicted that the vehicle separation when they are closest to each other is 0 or a certain margin distance, the vehicle separation of 0 or of a certain margin distance is permitted. Accordingly, there is the problem that the vehicle separation becomes inadequate in the case in which the preceding vehicle performs abrupt deceleration.